Dissertationen zum Thema „Non-Stationary conditions“

Brushless Direct Current (BLDC) motors are one of the motor types rapidly gaining popularity. BLDC motors are being increasingly used in critical high performance industries such as appliances, automotive, aerospace, consumer, medical, industrial automation equipment and instrumentation. Fault detection and condition monitoring of BLDC machines is therefore assuming a new importance. The objective of this research is to advance the field of rotor and load fault diagnosis in BLDC machines operating in a variety of operating conditions ranging from constant speed to continuous transient operation. This objective is addressed as three parts in this research. The first part experimentally characterizes the effects of rotor faults in the stator current and voltage of the BLDC motor. This helps in better understanding the behavior of rotor defects in BLDC motors. The second part develops methods to detect faults in loads coupled to BLDC motors by monitoring the stator current. As most BLDC applications involve non-stationary operating conditions, the diagnosis of rotor faults in non-stationary conditions forms the third and most important part of this research. Several signal processing techniques are reviewed to analyze non-stationary signals. Three new algorithms are proposed that can track and detect rotor faults in non-stationary or transient current signals.

Time-frequency methods are widely used tools to diagnose planetary gearbox fault under non-stationary conditions. However, the existing time-frequency methods still have some problems, such as smearing effect and cross-term interference, and these problems limit the effectiveness of the existing time-frequency methods in planetary gearbox fault diagnosis under non-stationary conditions. To address the aforementioned problems, four time-frequency methods are proposed in this thesis. As nowadays a large portion of the industrial equipment is equipped with tachometers, the first three methods are for the cases that the shaft rotational speed is easily accessible and the last method is for the cases of shaft rotational speed is not easily accessible. The proposed methods are itemized as follows: (1) The velocity synchronous short-time Fourier transform (VSSTFT), which is a type of linear transform based on the domain mappings and short-time Fourier transform to address the smear effect of the existing linear transforms under known time-varying speed conditions; (2) The velocity synchrosqueezing transform (VST), which is a type of remapping method based on the domain mapping and synchrosqueezing transform to address the smear effect of existing remapping methods under known time-varying speed conditions; (3) The velocity synchronous bilinear distribution (VSBD), which is a type of bilinear distribution based on the generalized demodulation and Cohen’s class bilinear distribution to address the smear effect and cross-term interference of existing bilinear distributions under known time-varying speed conditions and (4) The velocity synchronous linear chirplet transform (VSLCT), which is a non-parametric combined approach of linear transform and concentration-index-guided parameter determination to provide a smear-free and cross-term-free TFR under unknown time-varying speed conditions. In this work, simple algorithms are developed to avoid the signal resampling process required by the domain mappings or demodulations of the first three methods (i.e., the VSSTFT, VST and VSBD). They are designed to have different resolutions, readabilities, noise tolerances and computational efficiencies. Therefore, they are capable to adapt different application conditions. The VSLCT, as a kind of linear transform, is designed for unknown rotational speed conditions. It utilizes a set of shaft-rotational-speed-synchronous bases to address the smear problem and it is capable to dynamically determine the signal processing parameters (i.e., window length and normalized angle) to provide a clear TFR with desirable time-frequency resolution in response to condition variations. All of the proposed methods in this work are smear-free and cross-term-free, the TFRs generated by the methods are clearer and more precise compared with the existing time-frequency methods. The faults of planetary gearboxes, if any, can be diagnosed by identifying the fault-induced components from the obtained TFRs. The four methods are all newly applied to fault diagnosis. The effectiveness of them has been validated using both simulated and experimental vibration signals of planetary gearboxes collected under non-stationary conditions.

Faults in bearings usually manifest as marginal defects that intensify over time, allowing for well-informed preventative actions with early Fault Detection and Diagnosis (FDD) protocols. Detection of the fault begins with capturing, for example, acceleration signals from a machine. Traditionally, handpicked descriptive statistical features (mean, RMS, skewness, kurtosis, etc.) or spectral diagrams obtained from these signals are then used for FDD. However, machine signals are often generated under non-stationary operating conditions of varying loads and speeds, requiring further intervention. More advanced signal processing techniques (spectral kurtosis, or cyclostationary analysis) are hence used to account for the non-stationarity of the signal. This is usually done by separating acceleration signals into deterministic and random components. Fault detection in bearings is possible by observing the random components of the signal. A wealth of research has been invested in machine learning-based techniques to circumvent the problems associated with non-stationary signals. Many of these methods require vast amounts of historical data to train. Machines typically spend most of their life operating in a healthy condition, therefore, most historical data is occupied with data that comes from a healthy machine condition, training these methods is difficult, due to the shortage of data from a machine running in an unhealthy condition. Furthermore, well-performing machine learning algorithms still require a domain expert to extract features that are known to be fault sensitive. Deep learning is a recent approach in data analysis whereby feature extraction is incorporated within the training of the algorithm. The algorithm is given the ability to find and extract its features. The architecture of the algorithm allows for the extraction of complex hierarchical non-linear features. To the author’s knowledge, no attempt has been made to make full use of the power of deep learning together with the known structure of bearing acceleration signals to perform FDD. In this work, a bearing FDD methodology is developed using deep learning approaches. A model based on Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) is used to learn a lower-dimensional representation of an acceleration signal. A regularization strategy based on information maximization is used, which allows deterministic and random components of the signals to be learned separately. This representation is subsequently used to perform bearing FDD. The algorithm is trained in a completely unsupervised manner on exclusively healthy data and requires no preprocessing of that data. Furthermore, no auxiliary signals such as a shaft encoder, which contains information about the machine operating condition, is required for the algorithm to work. The methodology was tested on well-known benchmark datasets, and it was shown to be robust against non-stationary operating conditions. The algorithm can learn its fault metric and by observing the trajectory of the signal representation, it is also able to diagnose the type of fault.
Dissertation (MEng)--University of Pretoria, 2019.
Mechanical and Aeronautical Engineering
MEng
Unrestricted

Tradicionalmente, la detección de faltas en máquinas eléctricas se basa en el uso de la Transformada Rápida de Fourier ya que la mayoría de las faltas pueden ser diagnosticadas con ella con seguridad si las máquinas operan en condiciones de régimen estacionario durante un intervalo de tiempo razonable. Sin embargo, para aplicaciones en las que las máquinas operan en condiciones de carga y velocidad fluctuantes (condiciones no estacionarias) como por ejemplo los aerogeneradores, el uso de la Transformada Rápida de Fourier debe ser reemplazado por otras técnicas. La presente tesis desarrolla una nueva metodología para el diagnóstico de máquinas de inducción de rotor de jaula y rotor bobinado operando en condiciones no estacionarias, basada en el análisis de las componentes de falta de las corrientes en el plano deslizamiento frecuencia. La técnica es aplicada al diagnóstico de asimetrías estatóricas, rotóricas y también para la falta de excentricidad mixta. El diagnóstico de las máquinas eléctricas en el dominio deslizamiento-frecuencia confiere un carácter universal a la metodología ya que puede diagnosticar máquinas eléctricas independientemente de sus características, del modo en el que la velocidad de la máquina varía y de su modo de funcionamiento (motor o generador). El desarrollo de la metodología conlleva las siguientes etapas: (i) Caracterización de las evoluciones de las componentes de falta de asimetría estatórica, rotórica y excentricidad mixta para las máquinas de inducción de rotores de jaula y bobinados en función de la velocidad (deslizamiento) y la frecuencia de alimentación de la red a la que está conectada la máquina. (ii) Debido a la importancia del procesado de la señal, se realiza una introducción a los conceptos básicos del procesado de señal antes de centrarse en las técnicas actuales de procesado de señal para el diagnóstico de máquinas eléctricas. (iii) La extracción de las componentes de falta se lleva a cabo a través de tres técnicas de filtrado diferentes: filtros basados en la Transformada Discreta Wavelet, en la Transformada Wavelet Packet y con una nueva técnica de filtrado propuesta en esta tesis, el Filtrado Espectral. Las dos primeras técnicas de filtrado extraen las componentes de falta en el dominio del tiempo mientras que la nueva técnica de filtrado realiza la extracción en el dominio de la frecuencia. (iv) La extracción de las componentes de falta, en algunos casos, conlleva el desplazamiento de la frecuencia de las componentes de falta. El desplazamiento de la frecuencia se realiza a través de dos técnicas: el Teorema del Desplazamiento de la Frecuencia y la Transformada Hilbert. (v) A diferencia de otras técnicas ya desarrolladas, la metodología propuesta no se basa exclusivamente en el cálculo de la energía de la componente de falta sino que también estudia la evolución de la frecuencia instantánea de ellas, calculándola a través de dos técnicas diferentes (la Transformada Hilbert y el operador Teager-Kaiser), frente al deslizamiento. La representación de la frecuencia instantánea frente al deslizamiento elimina la posibilidad de diagnósticos falsos positivos mejorando la precisión y la calidad del diagnóstico. Además, la representación de la frecuencia instantánea frente al deslizamiento permite realizar diagnósticos cualitativos que son rápidos y requieren bajos requisitos computacionales. (vi) Finalmente, debido a la importancia de la automatización de los procesos industriales y para evitar la posible divergencia presente en el diagnóstico cualitativo, tres parámetros objetivos de diagnóstico son desarrollados: el parámetro de la energía, el coeficiente de similitud y los parámetros de regresión. El parámetro de la energía cuantifica la severidad de la falta según su valor y es calculado en el dominio del tiempo y en el dominio de la frecuencia (consecuencia de la extracción de las componentes de falta en el dominio de la frecuencia). El coeficiente de similitud y los parámetros de regresión son parámetros objetivos que permiten descartar diagnósticos falsos positivos aumentando la robustez de la metodología propuesta. La metodología de diagnóstico propuesta se valida experimentalmente para las faltas de asimetría estatórica y rotórica y para el fallo de excentricidad mixta en máquinas de inducción de rotor de jaula y rotor bobinado alimentadas desde la red eléctrica y desde convertidores de frecuencia en condiciones no estacionarias estocásticas.
Vedreño Santos, FJ. (2013). Diagnosis of electric induction machines in non-stationary regimes working in randomly changing conditions [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34177
TESIS

Condition monitoring is very important for critical assets such as gearboxes used in the power and mining industries. Fluctuating operating conditions are inevitable for wind turbines and mining machines such as bucket wheel excavators and draglines due to the continuous uctuating wind speeds and variations in ground properties, respectively. Many of the classical condition monitoring techniques have proven to be ine ective under uctuating operating conditions and therefore more sophisticated techniques have to be developed. However, many of the signal processing tools that are appropriate for uctuating operating conditions can be di cult to interpret, with the presence of incipient damage easily being overlooked. In this study, a cost-e ective diagnostic methodology is developed, using machine learning techniques, to diagnose the condition of the machine in the presence of uctuating operating conditions when only an acceleration signal, generated from a gearbox during normal operation, is available. The measured vibration signal is order tracked to preserve the angle-cyclostationary properties of the data. A robust tacholess order tracking methodology is proposed in this study using probabilistic approaches. The measured vibration signal is order tracked with the tacholess order tracking method (as opposed to computed order tracking), since this reduces the implementation and the running cost of the diagnostic methodology. Machine condition features, which are sensitive to changes in machine condition, are extracted from the order tracked vibration signal and processed. The machine condition features can be sensitive to operating condition changes as well. This makes it difficult to ascertain whether the changes in the machine condition features are due to changes in machine condition (i.e. a developing fault) or changes in operating conditions. This necessitates incorporating operating condition information into the diagnostic methodology to ensure that the inferred condition of the machine is not adversely a ected by the uctuating operating conditions. The operating conditions are not measured and therefore representative features are extracted and modelled with a hidden Markov model. The operating condition machine learning model aims to infer the operating condition state that was present during data acquisition from the operating condition features at each angle increment. The operating condition state information is used to optimise robust machine condition machine learning models, in the form of hidden Markov models. The information from the operating condition and machine condition models are combined using a probabilistic approach to generate a discrepancy signal. This discrepancy signal represents the deviation of the current features from the expected behaviour of the features of a gearbox in a healthy condition. A second synchronous averaging process, an automatic alarm threshold for fault detection, a gear-pinion discrepancy distribution and a healthy-damaged decomposition of the discrepancy signal are proposed to provide an intuitive and robust representation of the condition of the gearbox under uctuating operating conditions. This allows fault detection, localisation as well as trending to be performed on a gearbox during uctuating operation conditions. The proposed tacholess order tracking method is validated on seven datasets and the fault diagnostic methodology is validated on experimental as well as numerical data. Very promising results are obtained by the proposed tacholess order tracking method and by the diagnostic methodology.
Dissertation (MEng)--University of Pretoria, 2016.
Mechanical and Aeronautical Engineering
MEng
Unrestricted

Condition based maintenance is becoming increasingly popular in many industrial contexts, offering substantial savings and minimising accidental damage. When applied to rotating machinery, its most common tool is vibration analysis, which relies on well-established mathematical models rooted in the theory of cyclo-non-stationary processes. However, the extraction of diagnostic information from the real world vibration signals is a delicate task requiring the application of sophisticated signal processing techniques, tailored for specific machines operating under restricted conditions. Such difficulty in the current state of the art of vibration analysis forces the industry to apply methods with reduced diagnostic capabilities but higher adaptability. However in doing so most of the potential of vibration analysis is lost and advanced techniques become of use only for academic endeavours. The aim of this document is to reduce the gap between industrial and academic applications of condition monitoring, offering ductile and automated tools which still show high detection capabilities. Three main lines of research are presented in this document. Firstly, the implementation of stochastic resonance in an electrical circuit to enhance directly the analog signal from an accelerometer, in order to lower the computational requirements in the next digital signal processing step. Secondly, the extension of already well-established digital signal processing techniques, cepstral prewhitening and spectral kurtosis, to a wider range of operating conditions, proving their effectiveness in the case of non-stationary speeds. Thirdly, the main contribution of the thesis: the introduction of two novel techniques capable of separating the vibrations of a defective component from the overall vibrations of the machine, by means of a threshold in the amplitude spectrum. After the separation, the cyclic content of the vibration signal is extracted and the thresholded signals provide an enhanced detection. The two proposed methods, phase editing and amplitude cyclic frequency decomposition, are both intuitive and of low computational complexity, but show the same capabilities as more sophisticated state of the art techniques. Furthermore, all these tools have been successfully tested on numerically simulated signals as well as on real vibration data from different machinery, lasting from laboratory test rigs to wind turbines drive-trains and aircraft engines. So in conclusion, the proposed techniques are a promising step toward the full exploitation of condition based maintenance in industrial contexts.

We provide contributions to two classical areas of queueing. The first part of this thesis focuses on finding new conditions for a Markov chain on a general state space to be Harris recurrent, positive Harris recurrent or geometrically ergodic. Most of our results show that establishing each property listed above is equivalent to finding a good enough feasible solution to a particular optimal stopping problem, and they provide a more complete understanding of the role Foster's criterion plays in the theory of Markov chains. The second and third parts of the thesis involve analyzing queues from a transient, or time-dependent perspective. In part two, we are interested in looking at a queueing system from the perspective of a customer that arrives at a fixed time t. Doing this requires us to use tools from Palm theory. From an intuitive standpoint, Palm probabilities provide us with a way of computing probabilities of events, while conditioning on sets of measure zero. Many studies exist in the literature that deal with Palm probabilities for stationary systems, but very few treat the non-stationary case. As an application of our main results, we show that many classical results from queueing (in particular ASTA and Little's law) can be generalized to a time-dependent setting. In part three, we establish a continuity result for what we refer to as jump processes. From a queueing perspective, we basically show that if the primitives and the initial conditions of a sequence of queueing processes converge weakly, then the corresponding queue-length processes converge weakly as well in some sense. Here the notion of convergence used depends on properties of the limiting process, therefore our results generalize classical continuity results that exist in the literature. The way our results can be used to approximate queueing systems is analogous to the way phase-type random variables can be used to approximate other types of random variables.

Machinery condition monitoring techniques are carried out based on the knowledge of the characteristics of signals obtained from a machine or plant. These signals are often non stationary signals whose frequency changes over time due to the time-varying natures of machine operations and fault effects. Conventional signal processing techniques are developed based on stationary signals and cannot reveal the time information of the frequency changes. The work undertaken in this research presents a generic study of non-stationary signal processing for machinery condition monitoring. Starting with examining the concept of non-stationary signals, it can be identified that most condition monitoring signals fall into two main categories: weak non-stationary signals, such as motor electrical current signal and strong non-stationary signal such as machinery vibration and acoustic signals. For developing techniques to process these two typical non-stationary signals, two experiments were carried out to obtain these them. Firstly, an induction motor drive system was set up based on a two-stage reciprocating compressor; the motor current signals were then acquired for compressor fault detection and diagnosis. Secondly, a set of vibration and acoustic measurement instrumentation was set up based on a diesel engine test system. The engine vibration and acoustic signals were collected for further analysis for engine combustion condition monitoring. The engine was fuelled by different biofuels during data collection allowing a new and efficient method of verifying different sustainable fuels to be developed based non intrusive vibro-acoustic measurements in conjunction with non-stationary signal analysis methods. A time domain based method, dynamic time warping, was validated and improved for analysing the motor current signal to detect and classify the common faults of reciprocating compressors. Based on the limitations of classical dynamic time warping, a phase estimation and compensation approach is developed to reduce the singularity effect of classical dynamic time warping in order to obtain accurate diagnostic results. A sliding window was also designed to improve computing efficiency. The diagnostic results show that the accuracy and reliability of detection and classification by the proposed dynamic time warping method is higher than that from Fourier transform spectrum and envelope analysis. In addition, the fault detection and classification is based on a root mean square (RMS) linear classifier processes combined with the proposed dynamic time warping method, and is based entirely on time domain analysis which is easier to apply to a real-time condition monitoring system. It was proved that the proposed dynamic time warping is a novel and efficient method for cyclostationary/weak non-stationary analysis. Various non-stationary signal processing techniques based on time-frequency domain analysis, including Wigner-Ville distribution, fractional Fourier transform and continuous wavelet transform, are investigated to process the engine vibration and the acoustic signals for the condition monitoring of engine combustion. A sound pressure level (SPL) indicator is designed based on the Wigner-Ville distribution (WVD) analysis and the fractional Fourier transform filtering of the engine vibro-acoustic signals. The processing results demonstrate that the combustion induced acoustics can be extracted for the diagnostics of engine combustion process and for condition monitoring. A root mean square (RMS) linear classifier is developed based on the engine acoustic analysis by time synchronous average and continuous wavelet transform, the classification demonstrates that the root mean square (RMS) values of the continuous wavelet transform coefficients can be used to evaluate the fuel for engine combustion and indicate the engine operating conditions. The analysis results verify that the engine vibro-acoustics have the potential to be used to diagnose the engine combustion process and to monitor the engine operating conditions with the application of suitable non-stationary signal processing techniques. This can be used instead of the cylinder pressure data which is both intrusive and costly to obtain. Finally, the conclusions and achievements are given based on the entirety of this research work, and suggestions are presented for further research.

Cette thèse est centrée autour de l'étude théorique et de l'analyse numérique des équations paraboliques non linéaires avec divers conditions aux limites. La première partie est consacrée aux équations paraboliques dégénérées mêlant des phénomènes non-linéaires de diffusion et de transport. Nous définissons des notions de solutions entropiques adaptées pour chacune des conditions aux limites (flux nul, Robin, Dirichlet). La difficulté principale dans l'étude de ces problèmes est due au manque de régularité du flux pariétal pour traiter les termes de bords. Ceci pose un problème pour la preuve d'unicité. Pour y remédier, nous tirons profit du fait que ces résultats de régularités sur le bord sont plus faciles à obtenir pour le problème stationnaire et particulièrement en dimension un d'espace. Ainsi par la méthode de comparaison "fort-faible" nous arrivons à déduire l'unicité avec le choix d'une fonction test non symétrique et en utilisant la théorie des semi-groupes non linéaires. L'existence de solution se démontre en deux étapes, combinant la méthode de régularisation parabolique et les approximations de Galerkin. Nous développons ensuite une approche directe en construisant des solutions approchées par un schéma de volumes finis implicite en temps. Dans les deux cas, on combine les estimations dans les espaces fonctionnels bien choisis avec des arguments de compacité faible ou forte et diverses astuces permettant de passer à la limite dans des termes non linéaires. Notamment, nous introduisons une nouvelle notion de solution appelée solution processus intégrale dont l'objectif, dans le cadre de notre étude, est de pallier à la difficulté de prouver la convergence vers une solution entropique d'un schéma volumes finis pour le problème de flux nul au bord. La deuxième partie de cette thèse traite d'un problème à frontière libre décrivant la propagation d'un front de combustion et l'évolution de la température dans un milieu hétérogène. Il s'agit d'un système d'équations couplées constitué de l'équation de la chaleur bidimensionnelle et d'une équation de type Hamilton-Jacobi. L'objectif de cette partie est de construire un schéma numérique pour ce problème en combinant des discrétisations du type éléments finis avec les différences finies. Ceci nous permet notamment de vérifier la convergence de la solution numérique vers une solution onde pour un temps long. Dans un premier temps, nous nous intéressons à l'étude d'un problème unidimensionnel. Très vite, nous nous heurtons à un problème de stabilité du schéma. Cela est dû au problème de prise en compte de la condition de Neumann au bord. Par une technique de changement d'inconnue et d'approximation nous remédions à ce problème. Ensuite, nous adaptons cette technique pour la résolution du problème bidimensionnel. A l'aide d'un changement de variables, nous obtenons un domaine fixe facile pour la discrétisation. La monotonie du schéma obtenu est prouvée sous une hypothèse supplémentaire de propagation monotone qui exige que la frontière libre se déplace dans les directions d'un cône prescrit à l'avance.

Le bon fonctionnement des machines tournantes repose sur la surveillance vibratoire de composants rotatifs fragiles tels que les engrenages et les roulements. Concernant plus particulièrement le cas des systèmes de transmission de puissance en aéronautique, la surveillance vibratoire présente des défis considérables qui sont abordés dans cette thèse : (i) les régimes de fonctionnement non stationnaires, qui nécessitent l'adoption d'approches synchrones, (ii) les interactions complexes entre différents sous-systèmes, susceptibles de masquer ou perturber les signaux de diagnostic et (iii) le bruit émis par diverses sources, tant environnementales qu’internes, rendant la détection des défauts plus difficile. Pour répondre à ces défis, les principes de diagnostic proposé dans cette thèse s'articulent autour de plusieurs objectifs : (1) une estimation fiable de la vitesse angulaire instantanée, permettant la synchronisation des signaux avec les variations du régime, (2) l'extraction des composantes vibratoires pertinentes pour isoler les composants mécaniques critiques et (3) l'application de diagnostics spécifiques à chaque composant, tenant compte des variations opérationnelles pour garantir robustesse et fiabilité. Les méthodologies développées sont validées par des données expérimentales, démontrant leur potentiel pour améliorer la fiabilité et la sécurité des systèmes de transmission en aéronautique
The proper functioning of rotating machines relies on vibration monitoring of fragile rotating components such as gears and bearings. Concerning more particularly the case of power transmission systems in aeronautics, vibration monitoring presents considerable challenges that are addressed in this thesis: (i) nonstationary operating regimes, which require the adoption of synchronous approaches, (ii) complex interactions between different subsystems, likely to mask or disturb diagnostic signals and (iii) noise emitted by various sources, both environmental and internal, making fault detection more difficult. To address these challenges, the diagnostic principles proposed in this thesis are structured around several objectives: (1) a reliable estimation of the instantaneous angular speed, allowing the synchronization of the signals with the variations of the regime, (2) the extraction of the relevant vibration components to isolate the critical mechanical components and (3) the application of specific diagnostics to each component, taking into account the operational variations to guarantee robustness and reliability. The developed methodologies are validated by experimental data, demonstrating their potential to improve the reliability and safety of transmission systems in aeronautics

Wnioskowanie statystyczne dla nieznanych rozkładów statystyk lub estymatorów można oprzeć na rozkładach asymptotycznych. Niestety, w przypadku danych zależnych, takie procedury statystyczne są¸ niejednokrotnie nieefektywne. Różne są¸ tego przyczyny, np. zbyt ma la liczba danych, nieznana postać rozkładu asymptotycznego, zbyt wolna zbieżność do rozkładu asymptotycznego. Od początku lat osiemdziesiątych ubiegłego wieku intensywnie prowadzone są badania nad rozwojem tzw. metod resamplingowych. Za pomocą tychże metod można bezpośrednio przybliżać nieznane rozkłady statystyk i estymatorów. Idea resamplingu jest prosta. Obliczamy replikacje estymatora i z tych replikacji wyznaczamy rozkład empiryczny tzw. rozkład resamplingowy. Problem, z którym trzeba się zmierzyć badając procedury resamplingowe to ich zgodność, tzn. czy rozkład resamplingowy jest bliski prawdziwemu rozkładowi ? Metod resamplingowych jest wiele. Ich zgodność w przypadku obserwacji niezależnych została dogłębnie zbadana. Przypadek danych stacjonarnych ze swoistą strukturą zależności tzn. silnie mieszających także został zbadany. Przedmiotem intensywnych prac badaczy był również resampling dla niestacjonarnych szeregów czasowych ze specyficzną formą niestacjonarności tzn. okresowych i prawie okresowych. Ostatnie badania nad metodami resamplingowymi koncentrują się głównie na szeregach czasowych ze zdefiniowana¸ przez Paula Doukhana słabą zależnością. W niniejszej pracy został przedstawiony model dla szeregów czasowych, które maja¸ bardzo specyficzne własności tzn.: posiadają długa¸ pamięć, ciężkie ogony (stabilne lub GED) oraz strukturę okresową. Taki model może mieć naturalne zastosowanie w wielu dziedzinach np.: energetyce, wibromechanice, telekomunikacji, klimatologii jak również w ekonomii. Celem pracy jest pokazanie twierdzeń dotyczących zgodności estymatora jednej z metod resamplingowych dla funkcji średniej we wspomnianych powyżej szeregach czasowych. Okazuje się, że jedyną metodą resamplingową, którą można zastosować do danych z długą pamięcią jest subsampling. Polega ona na wyborze z obserwacji wszystkich możliwych podciągów o pewnej długości i wyznaczaniu estymatora na tych podciągach. W pracy sformułowano i udowodniono centralne twierdzenia graniczne, niezbędne do udowodnienia zgodności subsamplingu. Ponadto przedstawiony został przegląd dotychczasowych rezultatów dotyczących metod resamplingowych w szeregach czasowych.

Thesis (M.S.) -- University of Maryland, College Park, 2004.
Thesis research directed by: Dept. of Civil and Environmental Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

Cette thèse propose trois méthodes de traitement du signal orientées vers la surveillance d’état et le diagnostic. Les techniques proposées sont surtout adaptées pour la surveillance d’état, effectuée à la base de vibrations, des machines tournantes qui fonctionnent dans des conditions d’opération non-stationnaires comme par exemple les éoliennes mais elles ne sont pas limitées à un tel usage. Toutes les méthodes proposées sont des algorithmes automatiques et gérés par les données.La première technique proposée permet de sélectionner la partie la plus stationnaire d’un signal en cadrant la représentation temps-fréquence d’un signal.La deuxième méthode est un algorithme pour l’association des dispositions spectrales, des séries harmoniques et des séries à bandes latérales avec des fréquences caractéristiques provennant du cinématique d'un système analysé. Cette méthode propose une approche unique dédiée à l’élément roulant du roulement qui permet de surmonter les difficultés causées par le phénomène de glissement.La troisième technique est un algorithme de démodulation de bande latérale entière. Elle fonctionne à la base d’un filtre multiple et propose des indicateurs de santé pour faciliter une évaluation d'état du système sous l’analyse.Dans cette thèse, les méthodes proposées sont validées sur les signaux simulés et réels. Les résultats présentés montrent une bonne performance de toutes les méthodes
This thesis proposes a three signal-processing methods oriented towards the condition monitoring and diagnosis. In particular the proposed techniques are suited for vibration-based condition monitoring of rotating machinery which works under highly non-stationary operational condition as wind turbines, but it is not limited to such a usage. All the proposed methods are automatic and data-driven algorithms.The first proposed technique enables a selection of the most stationary part of signal by cropping time-frequency representation of the signal.The second method is an algorithm for association of spectral patterns, harmonics and sidebands series, with characteristic frequencies arising from kinematic of a system under inspection. This method features in a unique approach dedicated for rolling-element bearing which enables to overcome difficulties caused by a slippage phenomenon.The third technique is an all-sideband demodulation algorithm. It features in a multi-rate filter and proposes health indicators to facilitate an evaluation of the condition of the investigated system.In this thesis the proposed methods are validated on both, simulated and real-world signals. The presented results show good performance of all the methods

Ce travail de thèse traite de la détection des défauts mécaniques des roulements à billes par analyse de grandeurs mécaniques et électriques dans des machines synchrones à aimants permanents haute vitesse. Le domaine applicatif de ce travail concerne l'aéronautique. Généralement, pour surveiller l'état des roulements à billes dans un actionneur électrique, des mesures vibratoires sont réalisées. Elles permettent, en exploitant le spectre du signal vibratoire, de mettre facilement en évidence la détérioration du roulement. Cette méthode de surveillance est cependant relativement couteuse en termes d'instrumentation et le placement d'un capteur vibratoire dans des équipements à fort degré d'intégration est parfois difficile. Nous proposons dans ce mémoire d'utiliser d'autres grandeurs physiques prélevées sur le système pour réaliser la surveillance de ces défauts. Il peut s'agir de grandeurs mécaniques (vitesse, position par exemple) et de grandeurs électriques (courant statorique, courant onduleur par exemple). L'utilisation de données déjà disponibles dans l'équipement pour les besoins de la commande permet ainsi de supprimer le système d'acquisition vibratoire. A partir d'enregistrements temporels de données réalisées au cours de campagnes d'essais, nous proposons des méthodologies de traitement du signal permettant d'extraire automatiquement des informations sensibles au défaut à surveiller. L'idée finale est de construire des indicateurs de l'état de santé des roulements permettant de prendre « juste à temps » des décisions fiables relatives à la maintenance ou à la sécurisation de l'équipement. Pour construire ces indicateurs, les signatures spécifiques aux défauts de roulements sont étudiées de manière théorique et expérimentale, pour l'ensemble des grandeurs prélevées. Leurs propriétés sont mises en évidence, permettant ainsi de définir les bandes fréquentielles les plus contributives au diagnostic. L'extraction de ces signatures est réalisée dans le domaine fréquentiel selon plusieurs méthodes. Deux types d'indicateurs automatiques différents sont proposés. Le premier est construit directement à partir du spectre d'amplitude des grandeurs par extraction de l'amplitude des harmoniques dans des bandes fréquentielles particulières. Le second intègre une dimension statistique dans l'analyse en exploitant le caractère aléatoire de certains harmoniques pour détecter la présence du défaut. Des critères de comparaison sont définis et utilisés pour étudier les performances des indicateurs proposés pour deux campagnes d'essais avec des roulements artificiellement dégradés, pour différentes vitesses de fonctionnement et pour différents paramètres de réglage des indicateurs.

The inability to effectively hedge against unfavourable exchange rate movements, using the current forward exchange rate as the only guideline, is a key inhibiting factor of international trade. Market participants use the current forward exchange rate quoted in the market to make decisions regarding future exchange rate changes. However, the current forward exchange rate is not solely determined by the interaction of demand and supply, but is also a mechanistic estimation, which is based on the current spot exchange rate and the carry cost of the transaction. Results of various studies, including this study, demonstrated that the current forward exchange rate differs substantially from the realized future spot exchange rate. This phenomenon is known as the exchange rate puzzle. This study contributes to the dynamics of modelling exchange rate theories by developing an exchange rate model that has the ability to explain the realized future spot exchange rate and the exchange rate puzzle. The exchange rate model is based only on current (time t) economic fundamentals and includes an alternative approach of incorporating the impact of the interaction of two international financial markets into the model. This study derived a unique exchange rate model, which proves that the exchange rate puzzle is a pseudo problem. The pseudo problem is based on the generally excepted fallacy that current non–stationary, level time series data cannot be used to model exchange rate theories, because of the incorrect assumption that all the available econometric methods yield statistically insignificant results due to spurious regressions. Empirical evidence conclusively shows that using non–stationary, level time series data of current economic fundamentals can statistically significantly explain the realized future spot exchange rate and, therefore, that the exchange rate puzzle can be solved. This model will give market participants in the foreign exchange market a better indication of expected future exchange rates, which will considerably reduce the dependence on the mechanistically derived forward points. The newly derived exchange rate model will also have an influence on the demand and supply of forward exchange, resulting in forward points that are a more accurate prediction of the realized future exchange rate.
Thesis (Ph.D. (Risk management))--North-West University, Potchefstroom Campus, 2011.

This dissertation investigates the effectiveness of a two stage fault identification methodology for rotating machines operating under non-stationary conditions with the use of a single vibration transducer. The proposed methodology transforms the machine vibration signal into a discrepancy signal by means of smart feature selection and statistical models. The discrepancy signal indicates the angular position and relative magnitude of irregular signal patterns which are assumed to be indicative of gear faults. The discrepancy signal is also independent of healthy vibration components, such as the meshing frequency, and effects of fluctuating operating conditions. The use of the discrepancy signal significantly reduces the complexity of fault detection and diagnosis. The first stage of the methodology involves extracting smart instantaneous operating condition specific features, while the second stage requires extracting smart instantaneous fault sensitive features. The instantaneous operating condition features are extracted from the coefficients of the low frequency region of the STFT of the vibration signal, since they are sensitive to operating condition changes and robust to the presence of faults. Then the sequence of operating conditions are classified using a hidden Markov model (HMM). The instantaneous fault features are then extracted from the coefficients in the wavelet packet transform (WPT) around the natural frequencies of the gearbox. These features are the converse to the operating condition features,since they are sensitive to the presence of faults and robust to the fluctuating operating conditions. The instantaneous fault features are sent to a set of Gaussian mixture models (GMMs), one GMM for each identified operating condition which enables the instantaneous fault features to be evaluated with respect to their operating condition. The GMMs generate a discrepancy signal, in the angular domain, from which gear faults may be detected and diagnosed by means of simple analysis techniques. The proposed methodology is validated using experimental data from an accelerated life test of a gearbox operated under fluctuating load and speed conditions.
Dissertation (MEng)--University of Pretoria, 2015.
Mechanical and Aeronautical Engineering
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